the sum of two numbers is 40. when the greater number is divided by the smaller, the result is one more than one half the smaller number. what are the numbers? please explain how you got the answer :) thanks
2007-05-17 19:06:54 · 8 answers · asked by redhotninniepepper 2 in Science & Mathematics ➔ Mathematics
x+y=40
x=40-y-----(i)
suppose x>y
x/y=1+y/2
x=y+y^2/2-----(ii)
subs. i into ii
40-y=y+y^2/2
y^2/2+2y-40=0
y^2+4y-80=0
solve to get the answer for y
then find the corresponding value of x
2007-05-17 19:24:55 · answer #1 · answered by Maths Rocks 4 · 1⤊ 0⤋
let the numbers be a,b and let a>b
sum of two numbers is 40.
a+b=40
when a is divided by b the quotient is 1 more than one half of b
therefore a/b=1+b/2
a=b(1+b/2) substitute this in the first equation
b(1+b/2)+b=40
b+b^2/2+b=40
b^2+4b/2=40
b^2+4b=80
b^2+4b-80=0. if you solve this quadratic eqn you will get the values of a,b.
2007-05-17 19:37:01 · answer #2 · answered by brilliantwaz 2 · 0⤊ 0⤋
lol. k i haven't try this for so long so let see. i hate word problem just so you know.
so let say x is the smaller number and y is the greater one.
x+y=40
y/x=1+x/2
time 2x to both side
2y=2x+x^2
x^2+2x-2y=0
bring the other equation down and time it by 2.
2x+2y=80
now when you add the two equations you will get
x^2+4x=80
x^2+4x-80=0
if using the quadratic equation you will get -11.165 and 7.165. that are for the smaller number. i'm thing 7.165 is better. and then but back to the original equation.
x+y=40
y=32.835
now to check.
32.835/7.165=4.583
1+7.165/2=4.583
there you go.
2007-05-17 19:33:08 · answer #3 · answered by Anonymous · 0⤊ 0⤋
use the guess and test method its the easiest. i kno 30 + 10 give me 40 so im goin to try it. 30/10=3 i kno that cant be right because 3 isnt one greater than half of 10 so i try again, i dont want to give you the answer so your going to have to figure it out on your own i just thought i would tell you how you could go about solving it
2007-05-17 20:30:51 · answer #4 · answered by Anonymous · 0⤊ 0⤋
x > y
x + y = 40
x/y = y/2 + 1
2x = y² + 2y
2.(40 - y) = y² + 2y
y² + 4y - 80 = 0
y = [- 4 ± √(16 + 320)] / 2
y = [- 4 ±√(336)] / 2
y = 7.2 accepting positive value.
x = 40 - 7.2 = 32.8
Numbers are 32.8 and 7.2
(I would have thought a question like this would have yielded whole numbers.)
2007-05-17 20:04:40 · answer #5 · answered by Como 7 · 0⤊ 0⤋
let two numbers be x and y
x+y=40
let y be greater number
y/x = (x/2) +1
so (40-x)=x^2/2 +x
or x^2+4x-80=0
solve for the quadratic equation and get the answer.
2007-05-17 19:31:36 · answer #6 · answered by alien 4 · 0⤊ 0⤋
x big, y small
x+y=40
x/y=1 1/2
x/y=3/2
x=3y/2
x+y=40
3y/2+y=40
3y/2+2y/2=40
5y/2=40
5y=40x2
5y=80
y=80/5
y=16
x+y=40
x+16=40
x=40-16
x=24 ok
2007-05-17 19:32:20 · answer #7 · answered by sam 3 · 0⤊ 0⤋
O God! Praying for you!
2007-05-17 19:22:23 · answer #8 · answered by Anonymous · 0⤊ 0⤋